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A195368 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(2),sqrt(3),sqrt(5) right triangle ABC.

%I A195368 #9 Dec 24 2017 09:24:21
%S A195368 6,0,5,8,6,1,8,4,2,3,6,1,2,3,9,9,3,3,8,5,6,6,2,4,1,9,1,1,1,8,2,7,5,0,
%T A195368 7,5,0,6,7,8,1,8,6,5,3,3,5,1,4,6,6,2,8,3,1,7,5,5,5,7,8,8,3,5,9,2,6,5,
%U A195368 2,2,7,9,1,0,0,9,3,2,5,7,1,0,0,5,4,5,1,7,1,6,1,1,5,9,4,0,2,1,6,4
%N A195368 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(2),sqrt(3),sqrt(5) right triangle ABC.
%C A195368 See A195284 for definitions and a general discussion.
%H A195368 G. C. Greubel, <a href="/A195368/b195368.txt">Table of n, a(n) for n = 0..10000</a>
%e A195368 Philo(ABC,I)=0.6058618423612399338566241911182750750678...
%t A195368 a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
%t A195368 f = 2 a*b/(a + b + c);
%t A195368 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195368 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195368 x3 = f*Sqrt[2]
%t A195368 N[x1, 100]
%t A195368 RealDigits[%]    (* (A) A195365 *)
%t A195368 N[x2, 100]
%t A195368 RealDigits[%]    (* (B) A195366 *)
%t A195368 N[x3, 100]
%t A195368 RealDigits[%]    (* (C) A195367 *)
%t A195368 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195368 RealDigits[%]    (* Philo(ABC,I) A195368 *)
%Y A195368 Cf. A195284.
%K A195368 nonn,cons
%O A195368 0,1
%A A195368 _Clark Kimberling_, Sep 16 2011